Implementations of the claimed invention generally may relate to ray tracing and, more particularly, to interval arithmetic for ray tracing.
Ray tracing is a well know method used in modeling of a variety of physical phenomena related to wave propagation in various media. For example it is used for computing an illumination solution in photorealistic computer graphics, for complex environment channel modeling in wireless communication, aureal rendering in advanced audio applications, etc.
A ray is a half line of infinite length originating at a point in space described by a position vector which travels from said point along a direction vector. Ray tracing is used in computer graphics to determine visibility by directing one or more rays from a vantage point described by the ray's position vector along a line of sight described by the ray's direction vector. To determine the nearest visible surface along that line of sight requires that the ray be effectively tested for intersection against all the geometry within the virtual scene and retain the nearest intersection.
When working with real values, data is often approximated by floating-point (FP) numbers with limited precision. FP representations are not uniform through the number space, and usually a desired real value (i.e. ⅓) is approximated by a value that is less than or greater than the desired value. The error introduced is often asymmetrical—the difference between the exact value and the closest lower FP approximation may be much greater or less than the difference to the closest higher FP approximation. Such numerical errors may be propagated and accumulate though all the computations, sometimes creating serious problems.
One way to handle such numerical inaccuracies is to use intervals instead of FP approximations. In this case, any real number is represented by 2 FP values: one is less than the real one, and another is greater than the real one. The bound values are preserved throughout all computations, yielding an interval, which covers the exact solution. Usually, applications using interval arithmetic are limited to certain classes of workloads (such as quality control, economics or quantum mechanics) where the additional costs of such interval computations significantly outweigh the implications of dealing with inexact FP numbers for any final values.